Scalar (dot) product definition for JEE

Formula

\(\vec{a}\cdot\vec{b}=|\vec{a}|\,|\vec{b}|\cos\theta\)

Variables: \(\theta\) is the angle between \(\vec{a}\) and \(\vec{b}\), \(0\le \theta\le \pi\).

Conditions: For nonzero vectors when using angle form.

Angle between vectors, projections, orthogonality, work-like quantities.